{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ridge/LASSO polynomial regression with linear and random sampling\n",
    "* Input variable space is constructed using random sampling/cluster pick/uniform sampling\n",
    "* Linear fit is often inadequate but higher-order polynomial fits often leads to overfitting i.e. learns spurious, flawed relationships between input and output\n",
    "* Ridge and LASSO regression are used with varying model complexity (degree of polynomial)\n",
    "* Model score is obtained on a test set and average score over a # of runs is compared for linear and random sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global variables for the program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N_points = 41 # Number of points for constructing function\n",
    "x_min = 1 # Min of the range of x (feature)\n",
    "x_max = 10 # Max of the range of x (feature)\n",
    "noise_mean = 0 # Mean of the Gaussian noise adder\n",
    "noise_sd = 2 # Std.Dev of the Gaussian noise adder\n",
    "ridge_alpha = tuple([10**(x) for x in range(-3,0,1) ]) # Alpha (regularization strength) of ridge regression\n",
    "lasso_eps = 0.001\n",
    "lasso_nalpha=20\n",
    "lasso_iter=1000\n",
    "degree_min = 2\n",
    "degree_max = 8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate feature and output vector following a non-linear function\n",
    "$$ The\\ ground\\ truth\\ or\\ originating\\ function\\ is\\ as\\ follows:\\  $$\n",
    "\n",
    "$$ y=f(x)= x^2.sin(x).e^{-0.1x}+\\psi(x) $$\n",
    "\n",
    "$$: \\psi(x) = {\\displaystyle f(x\\;|\\;\\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}\\;e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_smooth = np.array(np.linspace(x_min,x_max,1001))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Linearly spaced sample points\n",
    "X=np.array(np.linspace(x_min,x_max,N_points))\n",
    "\n",
    "# Samples drawn from uniform random distribution\n",
    "X_sample = x_min+np.random.rand(N_points)*(x_max-x_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def func(x):\n",
    "    result = x**2*np.sin(x)*np.exp(-(1/x_max)*x)\n",
    "    return (result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "noise_x = np.random.normal(loc=noise_mean,scale=noise_sd,size=N_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = func(X)+noise_x\n",
    "y_sampled = func(X_sample)+noise_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Ideal y</th>\n",
       "      <th>y</th>\n",
       "      <th>X_sampled</th>\n",
       "      <th>y_sampled</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.761394</td>\n",
       "      <td>-1.566482</td>\n",
       "      <td>4.656746</td>\n",
       "      <td>-15.918912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.225</td>\n",
       "      <td>1.249025</td>\n",
       "      <td>0.973355</td>\n",
       "      <td>4.077757</td>\n",
       "      <td>-9.182027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.450</td>\n",
       "      <td>1.805456</td>\n",
       "      <td>3.668242</td>\n",
       "      <td>6.313265</td>\n",
       "      <td>2.500359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.675</td>\n",
       "      <td>2.360061</td>\n",
       "      <td>2.887801</td>\n",
       "      <td>3.218872</td>\n",
       "      <td>-0.052018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.900</td>\n",
       "      <td>2.825011</td>\n",
       "      <td>3.219761</td>\n",
       "      <td>2.033253</td>\n",
       "      <td>3.413888</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       X   Ideal y         y  X_sampled  y_sampled\n",
       "0  1.000  0.761394 -1.566482   4.656746 -15.918912\n",
       "1  1.225  1.249025  0.973355   4.077757  -9.182027\n",
       "2  1.450  1.805456  3.668242   6.313265   2.500359\n",
       "3  1.675  2.360061  2.887801   3.218872  -0.052018\n",
       "4  1.900  2.825011  3.219761   2.033253   3.413888"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(data=X,columns=['X'])\n",
    "df['Ideal y']=df['X'].apply(func)\n",
    "df['y']=y\n",
    "df['X_sampled']=X_sample\n",
    "df['y_sampled']=y_sampled\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the function(s), both the ideal characteristic and the observed output (with process and observation noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e1bf308e10>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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L5eLaa68GMoCH8m5NISIihri4ODVjl/PSvXt3kpOT+c9//uN0FJ9WkEKtHrAV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\nkiRJZer/AbafJyzBh3CNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1b657a860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter('X','Ideal y',title='Ideal y',grid=True,edgecolors=(0,0,0),c='blue',s=40,figsize=(10,5))\n",
    "plt.plot(x_smooth,func(x_smooth),'k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e1bf308cf8>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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M1q1bGx1HGKhHjx5kZmYyb948o6O4JMMLNaXULKXUGaXUvhzbSiulvlNKHbb8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\nERGfUqEmIiIi4lP/D2jcE2saeeUrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1bf30a828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter('X_sampled',y='y_sampled',title='Randomly sampled y',\n",
    "                grid=True,edgecolors=(0,0,0),c='orange',s=40,figsize=(10,5))\n",
    "plt.plot(x_smooth,func(x_smooth),'k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e1c1467588>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Uj+RooWat/R74+5q7mwMJIxPnAIEZGkpERK5r1KhRFCpUiBdffNHpKOImAgMD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c1462160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter('X',y='y',title='Linearly sampled y',grid=True,edgecolors=(0,0,0),c='orange',s=40,figsize=(10,5))\n",
    "plt.plot(x_smooth,func(x_smooth),'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import scikit-learn librares and prepare train/test splits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\cross_validation.py:41: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import LassoCV\n",
    "from sklearn.linear_model import RidgeCV\n",
    "from sklearn.ensemble import AdaBoostRegressor\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn.pipeline import make_pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df['X'], df['y'], test_size=0.33)\n",
    "X_train=X_train.values.reshape(-1,1)\n",
    "X_test=X_test.values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial model with Ridge regularization (pipelined) with lineary spaced samples\n",
    "** This is an advanced machine learning method which prevents over-fitting by penalizing high-valued coefficients i.e. keep them bounded **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 2: -0.04323708983722585\n",
      "\n",
      "Test score of model with degree 3: -0.04323708983722607\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 4: 0.09365803380879467\n",
      "\n",
      "Test score of model with degree 5: 0.2942094903725706\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 6: 0.5078727869614987\n",
      "\n",
      "Test score of model with degree 7: 0.6519272435828123\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 8: 0.6929923646710744\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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ITVjXFBlXXwyGm+hmg8V40o3Ut0jNbtZegtRD7lZSc/TzpC90NquLe9O5CcvMzOriGoiZ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\n8X4d+HdgU0mP5Sa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i1hgl/Qa4sVlx9KCl+6Q3ImJG9nu2pOtIzW13FxvVu16WNCoiZmZt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c340db38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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i5TZty2yJSonj8cdhm23aH4tZh6rVhPV74BbgdOCEXPnciJjd0qjMivKrX8HR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c340da58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kcdxxqdbh5GFWVS0J5GpJFwGDJH2WNDrhJY0Ny6xJPv/56nfGjYBf/7r58Zj1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\nM7O6/H+4HSCDiaXARgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c34d4358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iNaqYBLLC3d3MHMDMurX1BpEOq1u3cA2rbBtsAKtXJ08v0okV0wdyp5ldA3Q3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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c3569588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gIuaxeoiv2cBy663FE0QEHHJI/eMxa6BymrCWRURICgBJ69c4JrPmVCxx/P3v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\nxMzMKuIEYmZmFXECMTOzijiBmJlZRf4/3tYS42nipCQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c3665eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Nc08RsypU0om+EbCk4PESPD+VWf/KTR330kswciRnnHabbwFsTa+STvTfAPdI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c3665c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c36d2748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_sample_score = []\n",
    "poly_degree = []\n",
    "for degree in range(degree_min,degree_max+1):\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), RidgeCV(alphas=ridge_alpha,normalize=True,cv=5))\n",
    "    model = make_pipeline(PolynomialFeatures(degree), LassoCV(eps=lasso_eps,n_alphas=lasso_nalpha, \n",
    "                                                                  max_iter=lasso_iter,normalize=True,cv=5))\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), LinearRegression(normalize=True))\n",
    "    model.fit(X_train, y_train)\n",
    "    y_pred = np.array(model.predict(X_train))\n",
    "    test_pred = np.array(model.predict(X_test))\n",
    "    RMSE=np.sqrt(np.sum(np.square(y_pred-y_train)))\n",
    "    test_score = model.score(X_test,y_test)\n",
    "    linear_sample_score.append(test_score)\n",
    "    poly_degree.append(degree)\n",
    "    print(\"Test score of model with degree {}: {}\\n\".format(degree,test_score))\n",
    "    \n",
    "    #plt.figure()\n",
    "    #plt.title(\"RMSE: {}\".format(RMSE),fontsize=10)\n",
    "    #plt.suptitle(\"Polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    #plt.xlabel(\"X training values\")\n",
    "    #plt.ylabel(\"Fitted and training values\")\n",
    "    #plt.scatter(X_train,y_pred)\n",
    "    #plt.scatter(X_train,y_train)\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.title(\"Predicted vs. actual for polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    plt.xlabel(\"Actual values\")\n",
    "    plt.ylabel(\"Predicted values\")\n",
    "    plt.scatter(y_test,test_pred)\n",
    "    plt.plot(y_test,y_test,'r',lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.043237089837225851,\n",
       " -0.043237089837226073,\n",
       " 0.093658033808794672,\n",
       " 0.2942094903725706,\n",
       " 0.50787278696149873,\n",
       " 0.65192724358281229,\n",
       " 0.69299236467107439]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_sample_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modeling with randomly sampled data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df['X_sampled'], df['y_sampled'], test_size=0.33)\n",
    "X_train=X_train.values.reshape(-1,1)\n",
    "X_test=X_test.values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 2: -0.12434801463459723\n",
      "\n",
      "Test score of model with degree 3: -0.0769230959117706\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 4: 0.6735234335237947\n",
      "\n",
      "Test score of model with degree 5: 0.7969653226807432\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 6: 0.8321225592878035\n",
      "\n",
      "Test score of model with degree 7: 0.8124366657216142\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 8: 0.7813750489160156\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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EzMxq4gTSfy4oOoAuNGtc4Nhq0axxgWOrRbPGVRX3gZiZWU1cAzEz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c374eac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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n5L8844vSesIPf1iaPL7zndTDysnD+pBOayARca6kvwKfzoqOjoinahtW7dWy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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c38cd7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NgeUFz5dnZWbWkXK1jldeKX+9crMmVEkn+v8AD0o6XdLpwAPAlTWNyprW5Okt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\nRTHRJDcb57kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c398f5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Pe+5pfmwrkTKnOxKKFNvChTBwYGa5rumQCperCavxroODgY8SxsEC+BzwfDGD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c39f68d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AKyDdEz3ncKy3euEF2L7EAfV++7U/CjGzNio5D+T7ku4EWju+fzYiZtU2LJqB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\nTiBmZlYVJxAzM6vK/we8OMiYigdz2wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c3aeb9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uuw/22Sf3MFfrp0i5SqmBAKwCzHf3G82sl5lt4u5vVzIwd38AeKCSy5D2NXZi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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c3aeb6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GjAFmAPe5+/RyrlPabsSYmSuTR0ZD43JGjJmZUkTR3LmhjSNX8pg7N7RxKHmI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c3a8b0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_sample_score = []\n",
    "poly_degree = []\n",
    "for degree in range(degree_min,degree_max+1):\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), RidgeCV(alphas=ridge_alpha,normalize=True,cv=5))\n",
    "    model = make_pipeline(PolynomialFeatures(degree), LassoCV(eps=lasso_eps,n_alphas=lasso_nalpha, \n",
    "                                                                  max_iter=lasso_iter,normalize=True,cv=5))\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), LinearRegression(normalize=True))\n",
    "    model.fit(X_train, y_train)\n",
    "    y_pred = np.array(model.predict(X_train))\n",
    "    test_pred = np.array(model.predict(X_test))\n",
    "    RMSE=np.sqrt(np.sum(np.square(y_pred-y_train)))\n",
    "    test_score = model.score(X_test,y_test)\n",
    "    random_sample_score.append(test_score)\n",
    "    poly_degree.append(degree)\n",
    "    \n",
    "    print(\"Test score of model with degree {}: {}\\n\".format(degree,test_score))\n",
    "    \n",
    "    #plt.figure()\n",
    "    #plt.title(\"RMSE: {}\".format(RMSE),fontsize=10)\n",
    "    #plt.suptitle(\"Polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    #plt.xlabel(\"X training values\")\n",
    "    #plt.ylabel(\"Fitted and training values\")\n",
    "    #plt.scatter(X_train,y_pred)\n",
    "    #plt.scatter(X_train,y_train)\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.title(\"Predicted vs. actual for polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    plt.xlabel(\"Actual values\")\n",
    "    plt.ylabel(\"Predicted values\")\n",
    "    plt.scatter(y_test,test_pred)\n",
    "    plt.plot(y_test,y_test,'r',lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.12434801463459723,\n",
       " -0.0769230959117706,\n",
       " 0.67352343352379473,\n",
       " 0.79696532268074316,\n",
       " 0.83212255928780354,\n",
       " 0.81243666572161422,\n",
       " 0.78137504891601561]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_sample_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Linear sample score</th>\n",
       "      <th>Random sample score</th>\n",
       "      <th>degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.043237</td>\n",
       "      <td>-0.124348</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.043237</td>\n",
       "      <td>-0.076923</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.093658</td>\n",
       "      <td>0.673523</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.294209</td>\n",
       "      <td>0.796965</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.507873</td>\n",
       "      <td>0.832123</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.651927</td>\n",
       "      <td>0.812437</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.692992</td>\n",
       "      <td>0.781375</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Linear sample score  Random sample score  degree\n",
       "0            -0.043237            -0.124348       2\n",
       "1            -0.043237            -0.076923       3\n",
       "2             0.093658             0.673523       4\n",
       "3             0.294209             0.796965       5\n",
       "4             0.507873             0.832123       6\n",
       "5             0.651927             0.812437       7\n",
       "6             0.692992             0.781375       8"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_score = pd.DataFrame(data={'degree':[d for d in range(degree_min,degree_max+1)],\n",
    "                              'Linear sample score':linear_sample_score,\n",
    "                              'Random sample score':random_sample_score})\n",
    "df_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1e1c38ef780>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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a7rCU+lXcbn8yxlxujNkEZACbgQxjzCZjjLaFqqZLRGvbqwb5Zv0BLnptKenZ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\n/D+TGHpKHax6aAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e1c3b7cdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.grid(True)\n",
    "plt.plot(df_score['degree'],df_score['Linear sample score'],lw=2)\n",
    "plt.plot(df_score['degree'],df_score['Random sample score'],lw=2)\n",
    "plt.xlabel (\"Model Complexity: Degree of polynomial\",fontsize=20)\n",
    "plt.ylabel (\"Model Score: R^2 score on test set\",fontsize=15)\n",
    "plt.legend(fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cehcking the regularization strength from the cross-validated model pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.021486111550969477"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m=model.steps[1][1]\n",
    "m.alpha_"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
